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In mathematics, the disjoint union (or discriminated union) of the sets A and B is the set formed from the elements of A and B labelled (indexed) with the name of the set from which they come. So, an element belonging to both A and B appears twice in the disjoint union, with two different labels.
The disjoint union space X, together with the canonical injections, can be characterized by the following universal property: If Y is a topological space, and f i : X i → Y is a continuous map for each i ∈ I, then there exists precisely one continuous map f : X → Y such that the following set of diagrams commute:
The coproduct in the category of sets is simply the disjoint union with the maps i j being the inclusion maps.Unlike direct products, coproducts in other categories are not all obviously based on the notion for sets, because unions don't behave well with respect to preserving operations (e.g. the union of two groups need not be a group), and so coproducts in different categories can be ...
Geometric join of two line segments.The original spaces are shown in green and blue. The join is a three-dimensional solid, a disphenoid, in gray.. In topology, a field of mathematics, the join of two topological spaces and , often denoted by or , is a topological space formed by taking the disjoint union of the two spaces, and attaching line segments joining every point in to every point in .
Junta (governing body) (from Spanish), the name of various historical and current governments and governing institutions, including civil ones Military junta, one form of junta, government led by a committee of military officers; Junta (Habsburg), an administrative body that ruled in personal union with the Spanish Habsburgs
Additivity: If (X,A) is the disjoint union of a set of pairs (X α,A α), then the inclusions (X α,A α) → (X,A) induce an isomorphism from the direct sum: (,) (,) for every i. The axioms for a generalized cohomology theory are obtained by reversing the arrows, roughly speaking.
One common convention is to associate intersection = {: ()} with logical conjunction (and) and associate union = {: ()} with logical disjunction (or), and then transfer the precedence of these logical operators (where has precedence over ) to these set operators, thereby giving precedence over .
Juntas emerged in Spanish America as a result of Spain facing a political crisis due to the kidnapping and abdication of Ferdinand VII and Napoleon Bonaparte's invasion. . Spanish Americans reacted in much the same way the Peninsular Spanish did, legitimizing their actions through traditional law, which held that there was a retroversion of the sovereignty to the people in the absence of a ...